We know since the work of Sadi Carnot that the efficiency \(\eta\) (the fraction of heat converted into work) of a thermal engine cannot exceed a surprisingly simple maximum value, \(\eta_{\text{max}} = 1 - T_c/T_h\), defined in terms of the absolute temperatures of the cold and hot heat sources, \(T_c\) and \(T_h\). This limitation applies to a wide variety of devices, from combustion engines to solar cells: in the latter case, \(T_h \simeq 5800 \, \text{K}\) is that of the Sun and \(T_c\) is the ambient temperature, yielding \(\eta_{\text{max}} = 93\%\) [1].
We also know that living organisms can operate at (or even below) the temperature of their environment. In these conditions, Carnot's formula would yield zero efficiency, and thus no work production. And yet, our muscles can reach an efficiency of above 50% [2], higher than that of our cars! How can we solve this paradox?